with \(y_{-i}^{n+1} = y^{n+1} \setminus \lbrace y_i\rbrace \)  and \(\Psi : \mathbb {R}^n \times \mathbb {R}\rightarrow \mathbb {R}\)  a fixed function that is invariant to permutations in its first vector argument.
The function \(\Psi \)  is called a non-conformity measure, and the interpretation is that \(\psi _i(y^{n+1})\)  is small if and only if \(y_i\)  agrees with a prediction derived based on the data \(y_{-i}^{n+1}\) . The key references above give numerous examples of non-conformity measures; see, also, [1]} and [2]}. The basic idea is to define \(\psi _i(y^{n+1})\)  in such a way that it compares \(y_i\)  to a suitable summary of \(y_{-i}^{n+1}\) , for example
\(\psi _i(y^{n+1}) = |\text{average}(y_{-i}^{n+1}) - y_i|, \quad i \in I_{n+1}.\) 
